Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods

Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have important interpretations in real application of IFNs. In this paper, we will first review the existing methods for ranking and arithmetic operations on several representations of IFNs. Then, we will propose a new method based on arithmetic mean and geometric mean to compute membership and non-membership degrees of resulted IFN from arithmetic operations on IFNs. It is caused that the resulted degrees don't change monotonousness and be closer to reality. Furthermore, a new method for ranking of IFNs will be proposed. Finally, the proposed methods are used in the numerical examples, compared to some other existing methods.